# Questions tagged [kerr-metric]

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### Singularities of the Coordinate Systems

We know that, the singularity of the Schwarzschild metric at $r=2M$ can be removable via coordinate transformation to Kruskal-Szekers . Can we apply a similar argument to the Kerr metric? If so, what'...
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### Orbital Photon Speed at the equatorial plane of a rotating black hole

I've been trying to calculate $d\phi/dt$ of photons orbiting a Kerr black hole (Kerr metric in Boyer-Lindquist coordinates) on the equatorial plane, both counter and along with its rotation. So I used ...
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### Event horizon of a rotating black hole

For a non-rotating black hole, Schwarzschild radius itself forms the event horizon, but how do we find the event horizon of a rotating Kerr black hole?
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### What is the relative importance of the Coriolis term to the precession term in frame dragging by rotating Kerr black holes?

The Wikipedia entry for Thirring precession describes the Coriolis term as separate from the precession term. Is it fair to say that when looking at the dynamics of a rotating black hole, the ...
1answer
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### Light scattering on the rotating black hole in the Kerr geometry

To simulate light scattering on the rotating black hole we have used this paper and this code. First, we made animation for light beam scattering in the equatorial plane For not equatorial plane the ...
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### Where is the black hole horizon in ingoing Kerr coordinates?

In ingoing Kerr coordinates, the metric of the Kerr black hole spacetime is: \begin{equation} ds^2 = -\left(1-\frac{2Mr}{\Sigma}\right)dv^2 +\frac{2Mr}{\Sigma}\left(dr-a \mathrm{sin}^2\theta d\phi\...
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### Undefined symbol in Catalogue of Spacetimes (Kerr metric)

In the Catalogue of Spacetimes, in the Kerr metric section, under "General local tetrad", there is a cluster of four equations (strangely labeled 2.14.6a and 2.14.6b!), two of which contain ...
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### Exceeding the Kerr black hole spin limit

It is well known that the limit on the angular momentum for a Kerr black hole is given by \begin{equation} 0 \leq a^* \leq 1 \quad \text{where} \quad a^* \equiv \frac{cJ}{GM^2} \end{equation} and $J$ ...
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### Kerr metric in Eddington–Finkelstein form

I am searching for a reference in which I can find out the Kerr metric in Eddington–Finkelstein form. I have computed it by hand and I have obtained the following form but I am not sure above all of ...
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### GWs from Kerr BHs

A rotating neutron star can emit GW radiation if it has some ellipticity (Maggiore Gravitational Waves Vol I for example), even if we neglect spindown. I would think that a Kerr BH is not a spherical ...
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### Quasilocal formalism and computations in Kerr BH

I read an article about quasilocal formalism and calculations in a Kerr BH (this: https://arxiv.org/abs/hep-th/0102001). I was trying to reproduce the results obtained on it, but I found an expression ...
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### How does the angular velocity change with latitude in the Kerr metric?

I was told that in the Kerr metric for a black hole, the angular velocity of the horizon depends on the latitude. How exactly? Is it zero at the poles and largest at the horizon? Or is the dependence ...
1answer
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### Is possible to use black holes to propel a bullet or make a gun? [closed]

I was reading a book from my grandpa about Black Holes, and in one page it says that some objects can obtain some of the kinetic force from the black holes (in specific cases) and can propel ...
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### Can the effective singularity radius of a rotating black hole be measured?

Can the angular velocity of a black hole be measured? I found this article explaining how to measure the spin of a black hole can be measured, though I'm unclear whether 'spin' means angular velocity ...
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### Second fundamental form of Kerr timeslice in BL-coordinates

I want to compute the coefficients of the second fundamental form $K$ of a timeslice $\lbrace t=0\rbrace$ in the Kerr metric in Boyer-Lindquist coordinates. I tried to do this via the definition of ...
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### Gravitational Redshift in Kerr Spacetime

Well, suppose then Schwarschild black holes. Following the $$, we have the redshift factor: $$d\tau = \sqrt{1-\frac{2M}{r}}dt. \tag{1}$$ This factor have an physical interpretation to be the ...
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### Spin rotation of masses in a rotating gravitational field around a black hole

If a rotational gravitational field affects masses in the way the frame and body velocities are added together does it mean that as the rotation of the frame has a gradient of the perpendicular ...
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### Horizons and other special surfaces on Kerr metric

The Kerr metric is \begin{equation} ds^2 = - \big(1-\frac{2GMr}{\rho^2}\big)dt^2-\frac{2GMra}{\rho^2}\sin^2 \theta \big(dtd\phi+d\phi dt\big)+ \frac{\rho^2}{\Delta}dr^2+\rho^2 d\theta^2 + \frac{\sin^...
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### Trying to determine physically meaningful initial conditions for test particle around a Kerr black hole

I am working on some code for a test particle orbiting a Kerr black hole. I am trying to determine what the initial $\frac{d t}{d\tau}$ would be. On Wikipedia https://en.wikipedia.org/wiki/...
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### Symmetries of quasinormal modes of Kerr black hole

I have been reading this following paper on numerical evolution of the Teukolsky equation (see e.g. Eq 1 in their paper) for spin -2 fields about a spinning black hole (Kerr) solution. As the ...
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### Gravitational waves from collapsing rotating mass? [closed]

According to the Birkhoff’s theorem, a non-rotating mass does not radiate gravitational waves during a spherically symmetric collapse. There is, however, no equivalent of the Birkhoff’s theorem for a ...
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### Why do angular velocity deviates from Keplerian value close to a black hole?

The energy-momentum conservation equation in General Relativity is expressed as $T^{\mu\nu}_{\;\;;\nu}=0$ and by projecting this equation into the space normal to the four-velocity, we obtain the ...
1answer
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### Does matter take infinite time to leave a black hole?

To this question: Can a sufficiently large black hole be singularity-free? about the possibility of a sufficiently large black hole not containing a singularity John Rennie posted an answer ...
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### Time Derivative defined by Fermi transport in Kerr Space-Time

I have been studying 3+1 GR the last weeks. I have tried to comprehend Electrodynamics in curved space-time: 3+1 formulation (1982) Thorne McDonald I have studied another 3+1 GR book but it didn'...
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### Normal vectors and induced metric Kerr metric

Consider the Kerr metric given by: ds^2 = -(1-\frac{2GMr}{\rho^2})dt^2 - \frac{2GMar\sin^2{\theta}}{\rho^2}(dtd\phi+d\phi dt)+ \frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2+ \frac{\sin^2\theta}{\rho^2}[...
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### Particle falling into a Kerr black hole

Let's say that a particle starts a radial free fall towards a Kerr black hole with zero initial energy at $r\rightarrow\infty$. The initial angular momentum of the particle is zero ($p_\phi = 0)$. ...
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### Teukolsky-Starobinsky identities

The Teukolsky-Starobinsky identites relate solutions of the two Newman-Penrose scalars $\Psi_0$ and $\Psi_4$ around Kerr black holes. For example (here I am quoting Theorem 1 in Sec 81 of ...